Can this even be modeled? 3D modeling of flexible spheres in contact with one another
There is nothing to model really, you can use blenders primitive spheres, and position them procedurally by using the centre of the parent sphere as the pivot point of the first layer of children and constraining them to the radius of the parent. This way they will appear on the surface of the parent. 

The way you can create the spheres is creating a emitter sphere which would be at the origin of your parent sphere with a radius of: 
EmitterSpereRadius = ParentRad + childrenRad

Then create a particle system using the emitter sphere as the ... emitter, and creating the desired amount of particles which you will set to be emitted from the surface of the sphere rather than the volume. Turn off all forces acting upon the particles and they should stand still.

Now you can replace this particles with instance geometry (your children spheres) and you will have a parent sphere with it's children just about touching it's surface. (Note, that if you distributed your particles randomly, some children could be overlapping). 

Then as John Burrill suggested apply softbody dynamics to all spheres, make them collidable with each other and their parent, and apply a strong force filed to the children from the parent which would allow them only to encompass the parent, squashing against him and themselves...

Repeat the same process for more layers.

This would get you some results.
In the case that i haven't totally misunderstood the question, please ignore. :)